Computer-generated hologram and its fabrication process, reflector using a computer-generated hologram, and reflective liquid crystal display

ABSTRACT

The invention provides a computer-generated hologram which can be viewed in white at the desired viewing region and a reflective liquid crystal display using the same as a reflector. The computer-generated hologram H is designed to diffuse light having a given reference wavelength λ STD  and incident thereon at a given angle of incidence θ in a specific angle range. In a range of wavelengths λ min  to λ max  including the reference wavelength λ STD  wherein zero-order transmission light or zero-order reflection light of incident light on the computer-generated hologram at a given angle of incidence is seen in white by additive color mixing, the maximum diffraction angle β 2MIN  of incident light of the minimum wavelength λ MIN  in the wavelength range and incident at the angle of incidence θ is larger than the minimum diffraction angle β 1MAX  of incident light of the maximum wavelength λ MAX  in the wavelength range and incident at said angle of incidence θ.

This is a Divisional of application Ser. No. 11/405,558 filed Apr. 18,2006, which is a Divisional of application Ser. No. 10/808,469 filedMar. 25, 2004, now U.S. Pat. No. 7,054,044, which is a ContinuationApplication of U.S. application Ser. No. 09/866,605 filed, May 30, 2001,now U.S. Pat. No. 6,747,769. The entire disclosures of the priorapplications are considered part of the disclosure of the accompanyingDivisional application and are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to a computer-generatedhologram, and more particularly to a computer-generated hologramsuitable for use as a reflector and its fabrication process as well as areflective liquid crystal display using a computer-generated hologram.

Of a variety of display systems already put to practical use, liquidcrystal display systems have now wide applications because they havesome advantages of low power consumption, color display capability,low-profile size, and low weight.

Instead of LCDs, it is difficult to use other type of displays forterminal equipment having no other choice to rely on batteries oraccumulators.

However, LCDs cannot emit light by themselves; in other words,extraneous light or illumination light is necessary for viewing imagesirrespective of whether they are of the reflection type or thetransmission type.

However, the use of sufficiently bright illumination light goes againstthe valuable advantage of low power consumption. Accordingly, even whenillumination light is used, it is unreasonable to make use ofillumination having relatively high illuminance; whether the light usedis extraneous light or illumination light, how limited light iseffectively used is of vital importance.

The applicant has already filed patent applications (JP-A's 11-296054and 11-183716) to come up with computer-generated holograms having aphase distribution capable of diffracting obliquely incident light in apredetermined viewing region. Of both, JP-A 11-296054 discloses acomputer-generated hologram having a phase distribution for allowinglight incident thereon at an oblique angle of incidence to be diffractedinto the predetermined viewing region.

To fabricate these computer-generated holograms which are still found tohave the desired effects, however, it is required to use atime-consuming, inefficient fabrication process comprising the steps ofusing a computer to find phase distributions all over the hologramregion by computations, and making a relief pattern for the replicationof computer-generated holograms on the basis of computation results.

For photoetching in particular, it is preferable to make use of aphotomask fabrication system because precise exposure is needed.However, the photomask fabrication system has some disadvantages of highcost, severe fabrication conditions and extended fabrication time, inwhich the extended fabrication time in particular offers a graveproblem.

SUMMARY OF THE INVENTION

One object of the present invention is to provide a novelcomputer-generated hologram which can be viewed in white at the desiredviewing region, and a reflective liquid crystal display using the sameas a reflector.

Another object of the present invention is to eliminate a problem inassociation with the fabrication of a relief pattern forcomputer-generated hologram fabrication, and especially a time problemin connection with data processing on aligners for photoetching.

Throughout the present disclosure, the term “photoetching” is understoodto mean a photostep for providing the desired pattern to aphotosensitive material by means of laser light, electron beams or thelike and etching the pattern into a relief configuration.

Yet another object of the present invention is to provide acomputer-generated hologram which has improved optical diffractionefficiency, allows a master pattern to be easily obtained forreplication purposes, is easy to fabricate, and enables its reliefsurface to come into contact with the back surface of a lighttransmission display device as well as a reflective liquid crystaldisplay using the same as a reflector.

According to the first invention to achieve the aforesaid first object,there is provided a computer-generated hologram designed to diffuselight having a given reference wavelength and incident thereon at agiven angle of incidence in a specific angle range, characterized inthat, in a range of wavelengths including said reference wavelengthwherein zero-order transmission light or zero-order reflection lightincident on said computer-generated hologram at a given angle ofincidence is seen in white by additive color mixing, the maximumdiffraction angle of incident light of the minimum wavelength in saidrange and incident at said angle of incidence is larger than the minimumdiffraction angle of incident light of the maximum wavelength in saidrange and incident at said angle of incidence.

Preferably in this case, the computer-generated hologram comprises anarray of two-dimensionally arranged minute cells, wherein each cell hasan optical path length for imparting a unique phase to reflection lightor transmission light, and a phase distribution obtained by adding afirst phase distribution that substantially diffracts a verticallyincident light beam within a given viewing region and does notsubstantially diffract the light beam toward other region to a secondphase distribution that allows an obliquely incident light beam at agiven angle of incidence to leave the cell vertically.

Alternatively, the computer-generated hologram may comprise an array oftwo-dimensionally arranged minute cells, wherein each cell has anoptical path length for imparting a unique phase to reflection light ortransmission light as well as a phase distribution which substantiallydiffracts an obliquely incident light beam at a given angle of incidencewithin a given viewing region and does not substantially diffract thelight beam toward other region and which substantially diffracts avertically incident light beam within another region shifted from saidgiven viewing region and does not substantially diffract the light beamtoward a region except for said another region.

Practically, the cells are arranged in columns and rows just likecheckers.

Further, the computer-generated hologram may be a reflectioncomputer-generated hologram wherein a reflective layer is provided on arelief pattern provided on the surface of the substrate.

Further, the computer-generated hologram may be constructed in such away as to be adaptable to the minimum wavelength of 450 nm and themaximum wavelength of 650 nm.

Preferably, the computer-generated hologram should satisfy:λ_(MIN)/λ_(MAX)≧(sin β_(1STD)−sin θ)/(sin β_(2STD)−sin θ)  (11)where θ is the angle of incidence of illumination light, λ_(MIN) is theminimum wavelength, λ_(MAX) is the maximum wavelength, β_(1STD) is theminimum diffraction angle at a given reference wavelength λ_(STD) andβ_(2STD) is the maximum diffraction angle at the given referencewavelength λ_(STD).

It is also preferable that the computer-generated hologram satisfies:sin θ≧(λ_(MAX) sin β_(1STD)−λ_(MIN) sinβ_(2STD))/(λ_(MAX)−λ_(MIN))  (12)where θ is the angle of incidence of illumination light, λ_(MIN) is theminimum wavelength, λ_(MAX) is the maximum wavelength, β_(1STD) is theminimum diffraction angle at a given reference wavelength λ_(STD) andβ_(2STD) is the maximum diffraction angle at the given referencewavelength λ_(STD).

A display system of the invention is characterized by using any one ofthe aforesaid computer-generated holograms as a reflector.

One reflective liquid crystal display system of the invention ischaracterized in that any one of the aforesaid computer-generatedholograms is disposed as a reflector on the back surface thereof.

Another reflective liquid crystal display system of the invention ischaracterized in that any one of the aforesaid computer-generatedholograms is interposed as a reflector between a liquid crystal layerthereof and a back surface substrate thereof.

According to the invention to achieve the aforesaid first object, thecomputer-generated hologram is constructed such that, in a range ofwavelengths including the reference wavelength wherein zero-ordertransmission light or zero-order reflection light incident on thecomputer-generated hologram at a given angle of incidence is seen inwhite by additive color mixing, the maximum diffraction angle ofincident light of the minimum wavelength in said range and incident atsaid angle of incidence is larger than the minimum diffraction angle ofincident light of the maximum wavelength in said range and incident atsaid angle of incidence. Thus, the computer-generated hologram can beseen in white in the angle range defined between the maximum diffractionangle of the minimum wavelength and the minimum diffraction angle of themaximum wavelength, and there is no change in the color seen even whenthe viewer moves his eyes within that range. This computer-generatedhologram is suitable for reflector in reflective LCDs.

In one typical process for the fabrication of computer-generatedholograms used so far in the art, phase distributions are calculated allover the region of the hologram to be fabricated. Then, a large amountof data are entered into an aligner on the basis of the results ofcalculations for exposure processing. According to the inventionprovided to achieve the aforesaid second object, a computer-generatedhologram is constructed of an array of minute elemental hologram piecesarranged in columns and rows. Then, the calculation of the phasedistribution is performed only for the minute elemental hologram pieceby far smaller than the entire computer-generated hologram. Whenexposure is carried out for photoetching, too, a much smaller amount ofdata on the minute elemental hologram piece than before are used, sothat loads on the data processing on the aligner can be alleviated toreduce the overall exposure time. Thus, the twelfth invention providedto achieve the second object has been accomplished.

That is, the twelfth invention provided to achieve the second objectrelates to a computer-generated hologram comprising minute elementalhologram pieces closely arranged on a plane, characterized in that eachelemental hologram piece has an optical path length enough to impart anidentical phase distribution to reflection light or transmission light.

The thirteenth invention provided to achieve the second object andaccording to the twelfth invention relates to a computer-generatedhologram designed to diffuse light having a given reference wavelengthand incident thereon at a given angle of incidence in a specific anglerange, characterized in that, in a range of wavelengths including saidreference wavelength wherein zero-order transmission light or zero-orderreflection light incident on said computer-generated hologram at a givenangle of incidence is seen in white by additive color mixing, themaximum diffraction angle of incident light of the minimum wavelength insaid range and incident at said angle of incidence is larger than theminimum diffraction angle of incident light of the maximum wavelength insaid range and incident at said angle of incidence.

The fourteenth invention provided to achieve the second object andaccording to the twelfth or thirteenth invention relates to acomputer-generated hologram, characterized in that each elementalhologram piece has a phase distribution obtained by adding a first phasedistribution that substantially diffracts a vertically incident lightbeam within a given viewing region and does not substantially diffractthe light beam toward other region to a second phase distribution thatallows an obliquely incident light beam at a given angle of incidence toleave the elemental hologram piece vertically.

The fifteenth invention provided to achieve the second object andaccording to the twelfth or thirteenth invention relates to acomputer-generated hologram, characterized in that each elementalhologram piece a phase distribution which substantially diffracts anobliquely incident light beam at a given angle of incidence within agiven viewing region and does not substantially diffract the light beamtoward other region and which substantially diffracts a verticallyincident light beam within another region shifted from said givenviewing region and does not substantially diffract the light beam towarda region except for said another region.

The sixteenth invention provided to achieve the second object ischaracterized in that the computer-generated hologram according to anyone of the aforesaid twelfth to fifteenth inventions comprises a resinlayer including a hologram.

The seventeenth invention provided to achieve the second object ischaracterized in that the computer-generated hologram according to theaforesaid sixteenth invention further comprises a transparent substratefor supporting the resin layer including a hologram.

The eighteenth invention provided to achieve the second object ischaracterized in that the computer-generated hologram according to anyone of the aforesaid twelfth to seventeenth inventions is defined by arelief pattern on the surface of a hologram-forming layer.

The nineteenth invention provided to achieve the second object ischaracterized in that the computer-generated hologram according to theaforesaid eighteenth invention further comprises an optical reflectivelayer laminated on and along said relief pattern.

The 20th invention provided to achieve the second object ischaracterized in that in the aforesaid 18th invention, said opticalreflective layer is laminated on the other bare surface of saidhologram-forming layer which is free from said relief pattern.

The 21th invention provided to achieve the second object relates to areflector characterized by using the computer-generated hologramaccording to any one of the aforesaid 12th to 20th inventions.

The 22nd invention provided to achieve the second object relates to areflective liquid crystal display characterized in that thecomputer-generated hologram according to claim 10 is disposed on a backsurface thereof.

The 23rd invention provided to achieve the second object relates to areflective liquid crystal display characterized in that thecomputer-generated hologram according to the aforesaid 21st invention isinterposed between a liquid crystal layer and a back substrate in saidliquid crystal display.

The 24th invention provided to achieve the second object relates to acomputer-generated hologram fabrication process characterized bydefining a range which diffraction light obtained by diffraction ofincident light leaves, determining a hologram phase distribution forallowing said diffraction light to leave the defined range, quantizingthe determined phase distribution to find a quantized depth of ahologram relief, forming a relief on a substrate by photoetching on thebasis of the found quantized depth to obtain a relief pattern, andpatterning a resin layer using said relief pattern to form a hologramrelief on the surface of said resin layer.

The 25th invention provided to achieve the second object relates to acomputer-generated hologram fabrication process characterized bydefining a range which diffraction light obtained by diffraction ofincident light leaves, determining a hologram phase distribution forallowing said diffraction light to leave the defined range, quantizingthe determined phase distribution to find a quantized depth of ahologram relief and the number of steps of said depth, repeatingphotoetching given times corresponding to the obtained depth and thenumber of steps to form a relief pattern on an etching substrate, andpatterning a resin layer using said relief pattern to form a hologramrelief on the surface of said resin layer.

The 26th invention provided to achieve the second object relates to thecomputer-generated hologram fabrication process according to theaforesaid 24th or 25th invention, characterized in that said phasedistribution is determined per minute elemental hologram piece formingthe hologram, and said relief is formed on the basis of a phasedistribution obtained by repeatedly arranging a phase distribution ofsaid elemental hologram piece in a longitudinal direction of saidsubstrate.

The 27th invention provided to achieve the second object relates to thecomputer-generated hologram fabrication process according to any one ofthe aforesaid 24 to 26th inventions, characterized in that an opticalreflective layer is laminated on and along a relief side or other sideof said resin layer.

The 28th invention provided to achieve the second object relates to thecomputer-generated hologram fabrication process according to any one ofthe aforesaid 24th to 26th inventions, characterized in that the numberof steps L having the depth of said relief is the N-th power of 2 whereN is the number of photoetching cycles.

Reference is then made to a computer-generated hologram constructed toachieve the aforesaid third object of the present invention. Thiscomputer-generated hologram comprises a transparent plate materialhaving a light refractive index higher than that of air and a blazepattern of sawtoothed shape in section, which blaze pattern is disposedon the back surface of the transparent plate, and is designed in such away that the depth d of the blaze is equivalent to a half wavelength ord=λ/2n wherein λ is the wavelength of reference light and n is the lightrefractive index of the transparent plate. This computer-generatedhologram can provide solutions to prior art problems in conjunction withdiffraction efficiency, master pattern fabrication and replication andapplications. Thus, the present invention provides such acomputer-generated hologram as well as a reflector and a reflective LCDconstructed using the same.

The 29th invention provided to achieve the third object relates to acomputer-generated hologram characterized in that a blaze pattern ofsawtoothed shape in section is formed on a back side of a transparentsubstrate and the depth d of said blaze pattern is d=λ/2n where λ is thewavelength of reference light and n is the light refractive index of amaterial forming said transparent plate.

The 30th invention provided to achieve the third object relates to acomputer-generated hologram characterized in that a blaze pattern ofsawtoothed shape in section is formed on a back side of a transparentsubstrate with N steps having differences in level and the depth d ofsaid blaze pattern is d=λ/2n where λ is the wavelength of referencelight and n is the light refractive index of a material forming saidtransparent plate.

The 31st invention provided to achieve the third object relates to thecomputer-generated hologram according to the aforesaid 29th or 30thinvention, characterized in that an optical reflective layer islaminated on and along said blaze pattern formed on the back surface ofsaid transparent plate.

The 32nd invention provided to achieve the third object relates to thecomputer-generated hologram according to any one of the aforesaid 29thto 31st inventions, characterized in that the front surface of saidtransparent plate has been subject to antireflection treatment.

The 33rd invention provided to achieve the third object relates to areflector characterized by using the computer-generated hologramaccording to any one of the aforesaid 29th to 32nd inventions.

The 34th invention provided to achieve the third object relate to thereflector according to the aforesaid 33rd invention, characterized inthat a transparent adhesive layer is laminated on the front surface ofsaid transparent plate.

The 35th invention provided to achieve the third object relates to areflective-liquid crystal display characterized in that said frontsurface of the reflector according to the aforesaid 33rd invention is inclose contact with the back surface of said liquid crystal display.

The 36th invention provided to achieve the third object relates to areflective liquid crystal display characterized in that said frontsurface of the reflector according to the aforesaid 34th invention islaminated on the back surface of said liquid crystal display with saidtransparent adhesive layer interposed therebetween.

The 37th invention provided to achieve the third object relates to thereflective liquid crystal display according to the aforesaid 35th or36th invention, characterized in that a liquid crystal display deviceand said transparent plate in said reflector have a substantiallyidentical light refractive index, or said liquid crystal display device,said transparent adhesive layer and said transparent plate in saidreflector have a substantially identical light refractive index.

The 38th invention provided to achieve the third object relates to areflective liquid crystal display characterized in that thecomputer-generated hologram according to the aforesaid 33rd invention isinterposed between the liquid crystal layer and the back substrate insaid liquid crystal display with the front surface of saidcomputer-generated hologram opposite to said liquid crystal layer.

The 39th invention provided to achieve the third object relates to areflective liquid crystal display characterized in that said frontsurface of the reflector according to the aforesaid 33rd invention is inclose contact with the back surface of a light transmission display.

Still other objects and advantages of the invention will in part beobvious and will in part be apparent from the specification.

The invention accordingly comprises the features of construction,combinations of elements, and arrangement of parts which will beexemplified in the construction hereinafter set forth, and the scope ofthe invention will be indicated in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1( a), 1(b) and 1(c) are illustrative of a computer-generatedhologram comprising an array of elemental hologram pieces.

FIGS. 2( a) 2(b) and 2(c) are illustrative of some combinations ofelemental hologram pieces.

FIGS. 3( a), 3(b) and 3(c) are representations illustrative of someexamples of phase distributions for computer-generated holograms.

FIGS. 4( a) and 4(b) are illustrative of how a viewing position isshifted.

FIG. 5 is a flowchart illustrative of calculation steps for acomputer-generated hologram.

FIG. 6 is illustrative of the range of emergent light with respect toincident light.

FIGS. 7( a), 7(b) and 7(c) are illustrative of diffraction for eachwavelength in a narrow viewing range.

FIG. 8 is illustrative of diffraction of each wavelength in a narrowviewing range.

FIGS. 9( a), 9(b) and 9(c) are illustrative of diffraction for eachwavelength in a wide viewing range.

FIG. 10 is illustrative of diffraction of each wavelength in a wideviewing range.

FIG. 11 is illustrative of a phase distribution on the hologram surfaceof one embodiment of the computer-generated hologram according to theinvention.

FIG. 12 is illustrative of an amplitude distribution on a reconstructionplane when the computer-generated hologram of the FIG. 11 embodiment isvertically illuminated at the design wavelength.

FIG. 13 is illustrative of an amplitude distribution on a reconstructionplane when the computer-generated hologram of the FIG. 11 embodiment isobliquely illuminated at the reference wavelength.

FIG. 14 is illustrative of an amplitude distribution on a reconstructionplane when the computer-generated hologram of the FIG. 11 embodiment isobliquely illuminated at the minimum wavelength.

FIG. 15 is illustrative of an amplitude distribution on a reconstructionplane when the computer-generated hologram of the FIG. 11 embodiment isobliquely illuminated at the maximum wavelength.

FIG. 16 is illustrative in schematic form of the superposition ofvisible regions that are the distribution range of diffraction light inFIGS. 13 to 15.

FIG. 17 is a sectioned representation showing the construction of onereflective LCD according to the invention.

FIG. 18 a sectioned representation showing the construction of anotherreflective LCD to which the computer-generated hologram reflector of theinvention is applied.

FIG. 19( a) to 19(d) are illustrative of the photosteps for fabricatinga hologram relief pattern substrate.

FIGS. 20( a), 20(b) and 20(c) are illustrative of the number ofphotoetching cycles and the number of steps in the relief.

FIGS. 21( a) to 21(e) are illustrative of relief patterns and replicatedholograms.

FIGS. 22( a) and 22(b) are illustrative of liquid crystal displaydevices to which the computer-generated holograms of the invention areapplied.

FIGS. 23( a) and 23(b) are illustrative in section of anothercomputer-generated hologram of the invention.

FIGS. 24( a) to 24(e) are illustrative of blaze patterns and replicatedholograms.

FIGS. 25( a) and 25(b) are illustrative of liquid crystal displaydevices to which the computer-generated holograms of the invention areapplied.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The computer-generated hologram 1 according to the present invention isa composite or compound-eye array wherein computer-generated hologrampieces or minute elemental hologram pieces 2 are closely arranged on aplane.

The computer-generated hologram 1 of FIG. 1( a) is designed as a gridarray of square elemental hologram pieces 2 arranged in columns androws. As shown in FIG. 1( b), the square elemental hologram pieces 2 inan even row (e.g., the second or fourth row) may be shifted transverselywith respect to those in an odd row by a half pitch. Alternatively,elemental holograms 2 of rectangular slim shape may be closely arrangedside by side, as shown in FIG. 1( c).

In any of the aforesaid computer-generated holograms 1, all adjacentelemental hologram pieces 2 are the same. In other words, each hologrampiece 2 has an optical path length enough to impart the same phase toreflection light or transmission light.

Such computer-generated holograms 1 have a structure well suitable forreducing loads on a fabrication system; that is, the process offabricating the elemental hologram pieces 2 under the necessaryconditions is repeatedly carried out while a material forming thehologram 1 or a relief pattern for giving the hologram 1 is displaced,as will be described later.

FIGS. 2( a), 2(b) and 2(c) show a composite or compound-eyecomputer-generated hologram 1 comprising at least two types of minuteelemental hologram pieces 2.

Referring first to FIG. 2( a), two kinds of minute elemental hologrampieces 2 a and 2 b having different optical path lengths for impartingdifferent phases to reflection light or transmission light. As shown,one elemental hologram pieces 2 a are arranged every other in a rowwhile the other elemental hologram pieces 2 b are arranged betweenadjacent pieces 2 a. Thus, the elemental hologram pieces 2 used hereinmay be defined by such different sets of elemental hologram pieces.

It is here noted that the elemental hologram pieces 2 a and 2 b may bearranged in columns rather than in rows.

As shown in FIG. 2( b), three kinds of elemental hologram pieces 2 a, 2b and 2 c may be used in a group, and as shown in FIG. 2( c), oneelemental hologram piece 2 a may be surrounded with the other elementalhologram pieces 2 b.

Thus, if the computer-generated hologram 1 comprises a plurality ofgroups of different elemental hologram pieces, then the hologram 1 canpossess the respective properties of a plurality of elemental hologrampieces 2 a, 2 b, . . . .

As in the computer-generated holograms 1 of FIGS. 1( a) to 1(b), thecomputer-generated holograms 1 of FIGS. 2( a) to 2(b), too, have astructure well suitable for reducing loads on a fabrication system; thatis, the process of fabricating the elemental hologram pieces 2 under thenecessary conditions is repeatedly carried out while a material formingthe hologram 1 or a relief pattern for giving the hologram 1 isdisplaced, as will be described later.

The shape of each elemental hologram piece 2 used herein is notnecessarily limited to a quadrilateral such as a square or rectangle. Inother words, other polygonal elemental hologram pieces may be used. Forinstance, triangular elemental hologram pieces 2 can be closely arrangedin a row if one of adjacent hologram pieces is located inversely withrespect to the other and hexagonal elemental hologram pieces can beclosely arranged if pieces in one row are displaced by a half pitch withrespect to those in a row just below it, as shown in FIG. 1( b).

Alternatively, if octagonal elemental hologram pieces 2 are combinedwith square elemental hologram pieces 2 with their sides having the samelength as one side of the octagon, groups of two kinds of differentelemental hologram pieces can then be arranged.

Although not critical, the computer-generated hologram 1 of the presentinvention has usually a size of about 1 cm to about a few tens of cm.Each elemental hologram piece 2, of whatever type, has a size of about afew tens of pm to about 1 mm as an example. For instance, an elementalhologram piece 2 of 250 μm×250 μm in size accounts for 1/40,000 of acomputer-generated hologram 2 of 5 cm×5 cm in size.

In context of the computer-generated hologram 1 of the presentinvention, the “closely arranged elemental hologram pieces 2” isunderstood to mean an array of elemental hologram pieces 2 slightlyspaced away from one another, to say nothing of an array of elementalhologram pieces 2 brought in perfect contact with one another.

For the elemental hologram 2 in the computer-generated hologram 1 of thepresent invention, use is made of (1) the computer-generated hologramobtained on the basis of JP-A 11-187316, (2) the computer-generatedhologram obtained on the basis of JP-A 11-296054, and (3) the novelcomputer-generated hologram which can be viewed in white at the desiredviewing region and proposed by the present invention on the premise ofthe computer-generated hologram (1) or (2). In this regard, it isappreciated that this computer-generated hologram (3) may not only beused as the elemental holograms 2 and 2 a to 1 c of FIGS. 1 and 2 butmay also be used by themselves as a reflector having similar properties.

First of all, the computer-generated hologram (1) or (2) is explained.

The computer-generated hologram obtained on the basis of JP-A 11-187316comprises an array of two-dimensionally arranged minute cells. Each cellhas an optical path length enough to impart a unique phase to reflectionlight or transmission light, and a phase distribution obtained by addingthe first phase distribution that substantially diffracts a verticallyincident light beam within a given viewing region and does notsubstantially diffract the light beam toward other region to the secondphase distribution that allows an obliquely incident light beam at agiven angle of incidence to leave the cell vertically.

Here, the first phase distribution is a phase distribution for thecomputer-generated hologram which, when the hologram plane is verticallyilluminated with parallel light, diffracts the light to the givenviewing region alone. For instance, the first phase distribution may besuch a phase distribution φ_(HOLO) as illustrated in FIG. 3( a).

The second phase distribution is provided for a phase diffractiongrating which diffracts light incident from behind at an angle ofincidence θ in the forward direction. In other words, this is a phasedistribution φ_(GRAT) obtained by approximating such a phasedistribution as indicated by broken lines in FIG. 3( b) in the form of adigital step-formed function.

The phase distribution obtained by the addition of two such phasedistributions φ_(HOLO) and φ_(GRAT) provides the phase distribution φ ofthe computer-generated hologram set forth in JP-A 11-183716 and shown inFIG. 3( c), and the computer-generated hologram having this phasedistribution φ acts to diffract the light obliquely incident from behindat the angle of incidence θ toward the given viewing region in theforward direction.

Generally, a computer-generated hologram is found as follows.

Now consider a certain hologram. When the hologram plane is verticallyilluminated with parallel light at a reconstruction distance much largerthan the size of the hologram, the diffraction light obtained at thereconstruction plane is represented in terms of an amplitudedistribution at the hologram plane and the Fourier transform of a phasedistribution (Fraunhofer diffraction).

To impart given diffraction light to the reconstruction plane, acomputer-generated hologram positioned at the hologram plane has so farbeen found by a method therein the Fourier transform and inverse Fouriertransform are alternately repeated between the hologram plane and thereconstruction plane with the application of constraints. This method isknown as the Gerchberg-Saxton iterative algorithm method.

Here let h(x, y) represent the distribution of light at the hologramplane and f(u, v) indicate the distribution of light at thereconstruction plane. Then, these distributions of light are written as:h(x, y)=A _(HOLO)(x, y)exp(iφ _(HOLO)(x, y))  (1)f(u, v)=A _(IMG)(u, v)exp(iφ _(IMG)(u, v))  (2)where A_(HOLO)(x, y) is an amplitude distribution at the hologram plane,φ_(HOLO)(x, y) is a phase distribution at the hologram plane, A_(IMG)(u,v) is an amplitude distribution at the reconstruction plane andφ_(IMG)(u, v) is a phase distribution at the reconstruction plane.

Then, the aforesaid Fourier transform and inverse Fourier transform aregiven by

$\begin{matrix}{{f( {u,v} )} = {\underset{{- \infty}\mspace{20mu}}{\overset{\infty}{\int\int}}{h( {x,y} )}\exp\{ {- {{\mathbb{i}}( {{ux} + {vy}} )}} \}{\mathbb{d}x}{\mathbb{d}y}}} & (3) \\{{h( {x,y} )} = {\underset{{- \infty}\mspace{20mu}}{\overset{\infty}{\int\int}}{f( {u,v} )}\exp\{ {{\mathbb{i}}( {{ux} + {vy}} )} \}{\mathbb{d}x}{\mathbb{d}y}}} & (4)\end{matrix}$

Consider the case where using this Gerchberg-Saxton iterative algorithmmethod, a computer-generated hologram is obtained, which hologramdiffracts parallel light toward the given viewing region alone when thehologram plane is vertically illuminated with the parallel light.

For a better understanding of the following discussions, the amplitudedistribution A_(HOLO)(x, y) at the hologram plane is represented byA_(HOLO), the phase distribution φ_(HOLO)(x, y) at the hologram plane byφ_(HOLO), the amplitude distribution A_(IMG)(u, v) at the reconstructionplane by A_(IMG), and the phase distribution φ_(IMG)(u, v) at thereconstruction plane by φ_(IMG).

FIG. 5 is a flowchart to this end. At step (1), the hologram amplitudeA_(HOLO) and hologram phase φ_(HOLO) are initialized to 1 and a randomvalue, respectively, at hologram plane regions x₀≦x≦x₁ and y₀≦y≦y₁ inFIG. 6, and at step (2), the thus initialized values are subject to theaforesaid Fourier transform (3). If, at step (3), the amplitude A_(IMG)at the reconstruction plane, obtained by the Fourier transform, has asubstantially constant value within the given regions, e.g., u₀≦u≦u₁ andv₀≦v≦v₁, and becomes substantially zero within other regions, then theamplitude and phase initialized at step (1) provide a desiredcomputer-generated hologram.

If, at step (3), such conditions are not satisfied, then constraints areapplied at step (4). For instance, a value of 1 is imparted to theamplitude A_(IMG) at the reconstruction plane within the aforesaid givenregions and a value of 0 is applied within other regions, while thephase φ_(IMG) at the reconstruction plane is kept intact. After suchconstraints are applied, the aforesaid inverse Fourier transform (4) isapplied at step (5). At step (6), constraints are applied to the valueat the hologram plane, obtained by the inverse Fourier transform, totake the amplitude A_(HOLO) as 1 and allow the phase φ_(HOLO) to havemany values (bring the original function approximate to a digitalstep-formed function (quantization)). It is noted that when the phaseφ_(HOLO) is allowed to have a continuous value, such a multi-valuedphase is not always needed.

Then, the value is subjected to the Fourier transform at step (2). If,at step (3), the amplitude A_(IMG) at the reconstruction plane, obtainedby the Fourier transform, has a substantially constant value within thegiven regions, e.g., u₀≦u≦u₁ and v₀≦v≦v₁, and becomes substantially zerowithin other regions, then the amplitude and phase, to which theconstraints are applied at step (1), provide a desiredcomputer-generated hologram.

If, at step (3), such conditions are not satisfied, then the loop ofsteps (4)→(5)→(6)→(2)→(3) is repeated until the conditions for step (3)are satisfied (or converged), so that the final desiredcomputer-generated hologram can be obtained.

For an estimating function for indicating that the amplitude A_(IMG) atthe reconstruction plane is converged to a substantial given value atstep (3), for instance, the following expression (5) may be used.

However, the Σ (sum) with respect to u and v means the sum of the valuesat u₀≦u≦u₁ and v₀≦v≦v₁ for the cells in the hologram, and <A_(IMG)(v,v)> represents an ideal amplitude in the cell. For instance, when thisestimating function is 0.01 or less, the function is assumed to beconverged.

Alternatively, the following expression (6) using a difference betweenthe previous amplitude value and the present amplitude value in therepetition of the calculation loop may be used as the estimatingfunction.

Here A_(IMGi-1) is the previous amplitude value and A_(IMGi) is thepresent amplitude value.

$\begin{matrix}{{{Estimating}\mspace{14mu}{Function}} = {{1/N^{2}} \times {\sum\limits_{u,v}{{{A_{IMG}( {u,v} )} - ( {A_{{IMGi} - 1}( {u,v} )} )}}}}} & (5) \\{{{Estimating}\mspace{14mu}{Function}} = {{1/N^{2}} \times {\sum\limits_{u,v}{{{A_{IMGi}( {u,v} )} - {A_{{IMGi} - 1}( {u,v} )}}}}}} & (6)\end{matrix}$

From the thus found phase distribution, the depth distribution of anactual hologram is found. Regarding how to find the depth distribution,there is a difference between a reflection hologram and a transmissionhologram. When the hologram is of the reflection type, expression (7a)is used and when the hologram is of the transmission type, expression(7b) is used. In other words, φ of FIG. 3( c) (φ(x, y) in the followingexpressions) is transformed to the depth D of the computer-generatedhologram (D(x, y) in the following expressions).D(x, y)=λφ(x, y)/(4πn)  (7a)D(x, y)=λφ(x, y)/{2π(n ₁ −n ₀)}  (7b)Here (x, y) is the coordinates indicative of a position on the hologramplane, λ is the reference wavelength, n is the refractive index of thematerial forming the light incident side of the reflection surface inthe reflection hologram, and n₁ and n₀ are the refractive indices of thetwo materials forming the transmission hologram provided that n₁>n₀.

As will also be explained later, a relief pattern having a depth D(x, y)found from the aforesaid expressions (7a) and (7a) for each minute cellhaving a lengthwise x breadthwise size Δ is formed on the surface of ahologram-forming resin layer, with a given reflective layer laminatedthereon. The resultant hologram can be used as a hologram with enhancedeffects.

This Δ, for instance, is equivalent to the feed pitch of exposure light.

Reference is now made to the computer-generated hologram obtained on thebasis of JP-A 11-296054. This computer-generated hologram comprises anarray of two-dimensionally arranged minute cells. Each cell has anoptical path length enough to impart a unique phase to reflection lightor transmission light as well as a phase distribution that substantiallydiffracts an obliquely incident light beam at a given angle of incidencewithin a given viewing region and does not substantially diffract thelight beam toward other region and a phase distribution thatsubstantially diffracts a vertically incident light beam within anotherregion shifted from said given viewing region and does not substantiallydiffract the light beam toward a region except for said another region.

That is, a computer-generated hologram H is designed such that when thehologram plane is vertically illuminated with parallel light frombehind, the region at which the amplitude distribution A_(IMG)(u, v) atthe reconstruction plane is kept substantially constant is designated asthe range of u₀′≦u′≦u₁′ and v₀′≦v′≦v₁′ shifted from u₀≦u≦u₁ and v₀≦v≦v₁and the amplitude distribution A_(IMG)(u, v) becomes substantially zeroat other region ((u, v) is the coordinates on the reconstruction plane).

As shown in FIG. 4( a), a computer-generated hologram H is designed suchthat when parallel illumination light 3′ is vertically incident thereon,light is diffracted only to the range of u₀′≦u′≦u₁′ and v₀′≦v′≦v₁′ on areconstruction plane 4.

When the phase distribution φ_(HOLO)(x, y) of the computer-generatedhologram H is assumed to be a diffraction grating, diffraction by thecomputer-generated hologram H is represented by the following expression(8) that is a fundamental expression for the diffraction grating.sin θ_(d)−sin θ_(i) =mλ/d  (8)where m is the order of diffraction, d is the pitch of the diffractiongrating, λ is a wavelength, θ_(i) is the angle of incidence and θ_(d) isa diffraction angle.

From design conditions, θ_(i)=0 and α₀′≦θ_(d)≦α₁′. Here α₀′ is the angleof diffraction of light from the position of incidence to the positionof u₀′ at the reconstruction plane 4, and α₁′ is the angle ofdiffraction of light to the position of u₁′.

The case where parallel light 3 is obliquely incident on such acomputer-generated hologram H at the angle of incidence θ is shown inFIG. 4( b).

From the aforesaid fundamental expression (2) for the diffractiongrating, θ_(i)=θ in this case. Assuming that the embodiment shown ispositive, the range of diffraction angle θ_(d), α₀≦θ_(d)≦α₁, is shiftedfrom α₀′≦θ_(d)≦α₁′ to a smaller range, so that, as shown in FIG. 4( b),the diffraction range, u₀≦u_(d)≦u₁ (where u₀ is a position at whichdiffraction light is incident from the incidence position on thereconstruction plane 4 at a diffraction angel α₀, and u₁ is a positionat which diffraction light is incident thereon at a diffraction angleα₁), can be placed substantially in the forward direction with respectto the computer generated hologram H.

The same also goes for the v direction.

Thus, the computer-generated hologram H obtained on the basis of JP-A11-296054 is designed such that when parallel light is verticallyincident on the hologram plane from behind, the light is diffracted tothe forward, another region (u₀′≦u′≦u₁′ and v₀′≦v′≦v₁′) shifted from theforward given viewing region (u₀≦u≦u₁ and v₀≦v≦v₁), and when parallellight is obliquely incident on the hologram plane from behind, the lightis diffracted to the forward given viewing region (u₀≦u≦u₁ and v₀≦v≦v₁).

From the thus found phase distribution φ_(HOLO)(x, y), the depthdistribution of an actual hologram is found. When the hologram is of thereflection type, the aforesaid expression (7a) is used and when thehologram is of the transmission type, the aforesaid expression (7b) isused. A relief pattern having a depth D(x, y) found for each minute cellhaving a lengthwise x breadthwise size Δ is formed on the surface of ahologram-forming resin layer, with a given reflective layer laminatedthereon. The resultant hologram can be used as a hologram with enhancedeffects, as is the case with the computer-generated hologram on thebasis of JP-A 11-183716.

The phase distribution of the computer-generated hologram H may becalculated not only by the aforesaid methods themselves known so far inthe art but also by other methods, e.g., one set forth in JP-A 47-6591.

If required, the found phase distribution may be optimized by suitablemethods such as a hereditary algorithm or a simulated annealing method.

Reference is then made to the novel computer-generated hologram, hereinreferred to as (3), of the present invention, which can be seen in whiteat the desired viewing region.

The present invention provides a novel computer-generated hologramdesigned to diffuse light of a given reference wavelength incidentthereon at a given angle of incidence in a specific angle range,wherein:

in a range of wavelengths including said reference wavelength whereinzero-order transmission light or zero-order reflection light incident onsaid computer-generated hologram at said angle of incidence is seen inwhite by additive color mixing, the maximum diffraction angle ofincident light of the minimum wavelength in said range and incident atsaid angle of incidence is larger than the minimum diffraction angle ofincident light of the maximum wavelength in said range and incident atsaid angle of incidence.

For the sake of simplicity, an account is now given of a transmissioncomputer-generated hologram. However, it is noted that the presentinvention can also be applied to a reflection computer-generatedhologram.

FIGS. 7( a) and 7(b) are conceptual representations illustrative of howa narrow viewing region set for a computer-generated hologram H changeswith wavelengths.

Here assume that the reference wavelength λ_(STD) of illumination lightis between the minimum wavelength λ_(MIN) and the maximum wavelengthλ_(MAX). The computer-generated hologram H is designed with respect tothe reference wavelength λ_(STD).

As shown in FIG. 7( a), consider the case where illumination light 3entering the computer-generated hologram H at the reference wavelengthλ_(STD) and a certain oblique angle θ (which is an angle from the normalto the hologram H with the proviso that the counterclockwise angle ispositive) spreads as diffraction light 5 _(STD) in an angle range ofβ_(1STD) to β_(2STD) in the vicinity of the front. Numerical subscripts1 and 2 indicate the minimum diffraction angle and the maximumdiffraction angle, respectively. It is appreciated that the minimumdiffraction angle is the diffraction angle of diffraction light thatmakes the minimum angle with zero-order transmission light and themaximum diffraction angle is the diffraction angle of diffraction lightthat makes the maximum angle with the zero-order transmission light. Asillumination light 3 of the minimum wavelength λ_(MIN) enters thehologram H at the same oblique angle θ, a viewing region (the anglerange of β_(1MIN) to β_(2MIN)) to receive diffraction light 5 _(MIN) isshifted to a lower side (the zero-order transmission light side) ascompared with the incidence of the reference wavelength λ_(STD), asshown in FIG. 7( a), because the computer-generated hologram H is takenas being a cluster of phase diffraction gratings. As illumination light3 of the maximum wavelength λ_(MAX) enters the hologram H at the sameangle of incidence θ, on the other hand, a viewing region (the anglerange of β_(1MAX) to β_(2MAX)) to receive diffraction light 5 _(MAX) isshifted to an upper side (the side opposite to the zero-ordertransmission light side) as compared with the incidence of the referencewavelength λ_(STD), as shown in FIG. 7( c).

It is here noted that such a distribution of diffraction light asmentioned above is found within a plane including the normal to thehologram H and the illumination light 3. Within a plane including thenormal to the hologram H and perpendicular to that plane, however,diffraction light is distributed on both sides of the illumination light3.

In the absence of any region where all diffraction light 5 _(MIN), 5_(STD) and 5 _(MAX) overlap one another as shown in FIG. 8, there isthen no region to be viewed in white; the color to be viewed changeswith viewing positions (angles).

FIGS. 9( a), 9(b) and 9(c) are illustrative of how a wide viewing regionset for a computer-generated hologram H changes with wavelengths.

Upon the incidence of the minimum and maximum wavelengths λ_(MIN) andλ_(MAX) (FIGS. 9( b) and 9(c)), the viewing regions (the angle ranges ofβ_(1MIN) to β_(2MIN) and β_(1MAX) to β_(2MAX)) are shifted to a lowerand an upper side, respectively, as compared with the incidence of thereference wavelength λ_(STD), upon incidence of the minimum and maximumwavelengths λ_(MIN) and λ_(MAX), as in the case of the narrow viewingregion of FIGS. 7( a) to 7(c). However, the viewing region is so widethat when the hologram is viewed in the vicinity 6 of the front whereall diffraction light 5 _(MIN), 5 _(STD) and 5 _(MAX) overlap oneanother, all the wavelengths can be observed at the same time.

Accordingly, as long as the viewer moves within such a region, there isno substantial change in the color to be viewed.

The condition for setting the region 6 where all the assumed wavelengthscan be viewed is that, as can be seen from FIG. 10, the maximumdiffraction angle β_(2MIN) of the minimum wavelength λ_(MIN) in theassumed wavelength range is larger than the minimum diffraction angleβ_(1MAX) of the maximum wavelength λ_(MAX). When the diffraction light 5_(MIN), 5 _(STD) and 5 _(MAX) are distributed with respect to thezero-order diffraction light on the opposite side to that shown in FIGS.7 to 10, this relation is reversed; on the basis of the zero-orderdiffraction light, the maximum diffraction angle β_(2MIN) of the minimumwavelength λ_(MIN) with respect to the zero-order transmission light islarger than the minimum diffraction angle β_(1MAX) of the maximumwavelength λ_(MAX).

The sufficient condition for allowing all the wavelengths to overlap oneanother so that they can be viewed in white is that λ_(MIN)=450 nm andλ_(MAX)=650 nm. As far as at least the computer-generated hologram Hwith the maximum diffraction angle β_(2MIN) of the minimum wavelengthβ_(MIN)=450 nm being larger than the minimum diffraction angle β_(1MAX)of the maximum wavelength λ_(MAX)=650 nm is concerned, the hologram Hcan thus be viewed in white yet with no color change in the region 6.

From the foregoing, it is understood that for viewing all the desiredwavelengths in a certain viewing region, what is needed is only thedetermination of the viewing region λ_(1STD) to λ2_(STD) for thereference wavelength λ_(STD) according to the following steps.

At step (a), the angle of incidence θ of the reconstructing illuminationlight 3 is determined.

At step (b), the range 6 of the desired viewing angle at which thehologram is seen in white is determined. That is, the minimumdiffraction angle γ₁ (=β_(1MAX)) to the maximum diffraction angle γ₂(=β_(2MIN)) is determined. It is here noted that the minimum diffractionangle γ₁ and the maximum diffraction angle γ₂ are defined for thezero-order transmission light. In the distribution of FIGS. 7 to 10,θ<γ₁≦γ₂, and in the distribution opposite to that of FIGS. 7 to 10,θ>γ₁≧γ₂.

At step (c), the desired viewing wavelength is determined (the minimumwavelength λ_(MIN) to the maximum wavelength λ_(MAX)).

At step (d), the reference wavelength λ_(STD) is determined in the rangeof λ_(MIN)≦λ_(STD)≦λ_(MAX)).

At step (e), using the following expression (9) on the basis of thefundamental expression (8) for diffraction gratings, the minimumdiffraction angle β_(1STD) at the reference wavelength λ_(STD) is foundfrom the minimum diffraction angle γ₁ and the maximum wavelengthλ_(MAX).(sin γ₁−sin θ)/λ_(MAX)=(sin β_(1STD)−sin θ)/λ_(STD)sin β_(1STD)=sin θ+(sin γ₁−sin θ)×λ_(STD)/λ_(MAX)  (9)

At step (f), using the following expression (10) on the basis of thefundamental expression (8) for diffraction gratings, the maximumdiffraction angle β_(2STD) at the reference wavelength λ_(STD) islikewise found from the maximum diffraction angle γ₂ and the minimumwavelength λ_(MIN).(sin γ₂−sin θ)/λ_(MIN)=(sin β_(2STD)−sin θ)/λ_(STD)sin β_(2STD)=sin θ+(sin γ₂−sin θ)×λ_(STD)/λ_(MAX)  (10)

Then, a computer-generated hologram 1 is fabricated on the basis of JP-A11-183716 or JP-A 11-296054 in such a way that the minimum diffractionangle β_(1STD) and the maximum diffraction angle β_(2STD) are obtainableat the angle of incidence θ of illumination light and the referencewavelength λ_(STD), thereby obtaining a diffuse hologram wherein thewavelengths λ_(MIN) to λ_(MAX) can be viewed at the angle of incidence θof the reconstructing light illumination 3 in the viewing angle range ofγ₁ to γ₂ and so the hologram 1 can be seen in white.

Reference has been made to how to find the diffraction angle range ofβ_(1STD) to β_(2STD) used for calculations when the desired angle ofincidence θ of illumination light, the diffraction range of γ₁ to γ₂ andthe wavelength range of λ_(MIN) to λ_(MAX) are provided.

On the other hand, the condition for setting a region wherein, when theminimum diffraction angle β_(1STD) and the maximum diffraction angleβ_(2STD) are provided with respect to the reference wavelength λ_(STD)and the angle of incidence θ of illumination light, all light of thewavelength range of λ_(MIN) to λ_(MAX) can be simultaneously viewed andseen in white is given as follows, using the minimum diffraction angleβ_(1MAX)=γ₁ of the maximum wavelength λ_(MAX) and the maximumdiffraction angle β_(2MIN)=γ₂ of the minimum wavelength λ_(MIN).

(1) In the case where diffraction light exists on a positive side withrespect to the zero-order transmission light (FIG. 7 to FIG. 10),γ₂≧γ₁sin γhd 2≧sin γ₁

$\begin{matrix}{{{From}\mspace{14mu}{expressions}\mspace{14mu}(9)\mspace{14mu}{and}\mspace{14mu}(10)}{{{\sin\;\theta} + {( {{\sin\;\beta_{2{STD}}} - {\sin\;\theta}} ) \times {\lambda_{MIN}/\lambda_{STD}}}} \geq {{\sin\;\theta} + {( {{\sin\;\beta_{1{STD}}} - {\sin\;\theta}} ) \times {{\lambda_{MAX}/{\lambda_{STD}( {{\sin\;\beta_{2{STD}}} - {\sin\;\theta}} )}}/\lambda_{MIN}}}} \geq {( {{\sin\;\beta_{1{STD}}} - {\sin\;\theta}} ) \times \lambda_{MAX}}}{Since}{{\sin\;\beta_{2{STD}}} > {\sin\;\theta}}{{\lambda_{MIN}/\lambda_{MAX}} \geq {( {{\sin\mspace{11mu}\beta_{1{STD}}} - {\sin\;\theta}} )/( {{\sin\;\beta_{2{STD}}} - {\sin\;\theta}} )}}} & (11)\end{matrix}$

(2) In the case where diffraction light exists on a negative side withrespect to the zero-order transmission light (opposite to FIG. 7 to FIG.10),γ₂≦γ₁sin γ₂≦sin γ₁

$\begin{matrix}{{{{{From}\mspace{14mu}{expressions}\mspace{14mu}(9)\mspace{14mu}{and}\mspace{14mu}(10)}{\sin\;\theta} + {( {{\sin\;\beta_{2{STD}}} - {\sin\;\theta}} ) \times {\lambda_{MIN}/\lambda_{STD}}}} \leq {{\sin\;\theta} + {( {{\sin\;\beta_{1{STD}}} - {\sin\;\theta}} ) \times {{\lambda_{MAX}/{\lambda_{STD}( {{\sin\;\beta_{2{STD}}} - {\sin\;\theta}} )}}/\lambda_{MIN}}}} \leq {( {{\sin\;\beta_{1{STD}}} - {\sin\;\theta}} ) \times \lambda_{MAX}}}{Since}{{\sin\;\beta_{2{STD}}} < {\sin\;\theta}}{{\lambda_{MIN}/\lambda_{MAX}} \geq {( {{\sin\mspace{11mu}\beta_{1{STD}}} - {\sin\;\theta}} )/( {{\sin\;\beta_{2{STD}}} - {\sin\;\theta}} )}}} & (11)\end{matrix}$

Thus, expression (11) holds irrespective of whether the diffractionlight is on the positive side or on the negative side.

This expression (11) means that if the diffraction angle range ofβ_(1STD) to β_(2STD) at a certain reference wavelength λ_(STD) is set insuch a way as to meet expression (11) when the angle of incidence θ ofillumination light and the desired viewing wavelength range of λ_(MIN)to λ_(MAX) are provided, there is then a range of γ₁ to γ₂ where allwavelengths within the desired viewing wavelength range of λ_(MIN) toλ_(MAX) can be simultaneously viewed.

Transformation of expression (11) givessin θ≧(λ_(MAX) sin β_(1STD)−λ_(MIN) sinβ_(2STD))/(λ_(MAX)−λ_(MIN))  (12)

This expression (12) means that only when the angle of incidence θ ofillumination light is set in such a way as to meet expression (12) wherethe desired viewing wavelength range of λ_(MIN) to λ_(MAX) and thediffraction angle range of β_(1STD) to β_(2STD) at a certain referencewavelength λ_(STD) are provided, there is a range of γ₁ to γ₂ where allwavelengths within the desired viewing wavelength range of λ_(MIN) toλ_(MAX) can be simultaneously viewed.

The foregoing discussions have held true only for the plane includingthe normal to the computer-generated hologram H and illumination light3. Within a plane including the normal to the computer-generatedhologram H and perpendicular to the aforesaid plane, a distributionrange at the minimum wavelength λ_(MIN) provides a region that can beviewed in white. This is because within this plane, diffraction light isdistributed on both sides of illumination light. The range of thisregion may be determined by the transformation of the viewing region atthe reference wavelength λ_(STD), as mentioned above.

The technique for enabling the desired viewing region of the aforesaidcomputer-generated hologram H to be viewed in white may be used alone orin combination with the computer-generated hologram obtained on thebasis of the aforesaid JP-A 11-187316 wherein the light enteredobliquely from behind at the angle of incidence θ is diffracted towardthe given forward viewing region or the computer-generated hologramobtained on the basis of JP-A 11-296054 wherein light entered obliquelyfrom behind at the angle of incidence θ is diffracted toward the forwardgiven viewing region and vertically incident light is diffracted towardanother region shifted from the aforesaid given viewing region.

In any of the aforesaid cases (1) to (3), too, the depth D(x, y) isfound for each minute cell having a breadthwise×lengthwise size Δ, usingthe aforesaid expressions 7(a) and 7(b), as already mentioned. On thebasis of the results of this calculation, specific computer-generatedholograms H can be obtained.

To be more specific, a reflection hologram conforms to expression 7(a).A blaze hologram conforms to D(x, y)=λφ(x, y)/4πn, and a sawtoothed(binary) hologram conforms to D(x, y)=λφ(x, y)(N−1)/4πn. Here n is therefractive index of the material forming a transparent plate and N isthe number of steps in the sawtoothed hologram.

Reference is now made to one specific embodiment of the novelcomputer-generated hologram, herein referred to as (3), of the presentinvention, which can be viewed in white at the desired region. Acomputer-generated hologram H having such properties as shown in FIG. 10is divided into 32×32 square cells, and a reconstruction plane for anglerepresentation is divided into 32×32 square cells as well. In thisembodiment, the hologram plane has a phase distribution φ_(HOLO) asshown in FIG. 11. In this computer-generated hologram H, the phase ofeach cell is quantized in 16 steps between −π and +π. On the basis ofJP-A 11-296054, the computer-generated hologram H is assumed to bevertically illuminated with parallel light of 500 nm design wavelength.The then amplitude distribution A_(IMG) at the reconstruction plane isshown in FIG. 12. Diffraction light is diffracted in the desired rangeof 6×5.

FIG. 13 shows an amplitude distribution A_(IMG) at the reconstructionplane in the case of the reference wavelength λ_(STD)=500 nm, when thecomputer-generated hologram H is illuminated at a varied angle ofincidence of θ=−35°. It is found that the diffraction light isdistributed on a lower side as compared with the 0° incidence of FIG.12.

FIG. 14 shows an amplitude distribution A_(IMG) at the reconstructionplane when the computer-generated hologram H is illuminated At an angleof incidence of θ=−35° and the minimum wavelength of λ_(MIN)=400 nm. Itis seen that the diffraction light is distributed on a much lower side(the zero-order transmission light side) as compared with FIG. 13 at thereference wavelength of λ_(STD)=500 nm.

FIG. 15 shows an amplitude distribution A_(IMG) at the reconstructionplane when the computer-generated hologram H is illuminated at an angleof incidence of θ=−35° and the maximum wavelength of λ_(MAX)=700 nm. Itis seen that the diffraction light is distributed on an upper side (theside opposite to the zero-order transmission light side) as comparedwith FIG. 13 at the reference wavelength of λ_(STD)=500 nm.

FIG. 16 is illustrative of the superposition in schematic form ofvisible regions defined by the distribution ranges of diffraction lightin FIGS. 13 to 15. The diffraction angle in the longitudinal directionis indicated by β_(y) and the diffraction angle in the transversedirection by β_(x). As can be seen from FIG. 16, the visible region, inwhich light of all wavelengths in the wavelength range of 400 nm to 700nm can be viewed in the longitudinal direction, is defined between themaximum diffraction angle of the minimum wavelength and the minimumdiffraction angle of the maximum wavelength in the wavelength range. Inthe transverse direction, this visible region is defined by thediffraction angle range of the minimum wavelength.

It is noted that the aforesaid embodiment is provided only for thepurpose of specifically showing that the computer-generated hologram H,herein referred to as (3), can be calculated. In other words, anorder-of-magnitude number of cells must be calculated to construct anactual computer-generated hologram H.

The novel computer-generated hologram H, herein referred to as (3), ofthe present invention may be used by itself as a reflector which can beviewed in white at the desired viewing region.

If, as shown in FIG. 17 for the purpose of illustration alone, such acomputer-generated hologram H is used as a reflective diffuser 51 for areflective LCD, illumination light 52 incident on the LCD 40 from itsdisplay side is diffused and reflected to only the given viewing regionin the front, so that bright yet white displays can be presented in abright place without recourse to any spontaneous emission typebacklight. Referring to FIG. 17, the LCD 40 comprises a twisted nematicor other liquid crystal layer 45 sandwiched between two glass plates 41and 42. One glass plate 42 is provided on its inner surface with auniform opposite electrode 44 while another glass substrate 41 isprovided on its inner surface with a transparent display electrode 43independent for each pixel and a black matrix (not shown). Referringhere to a color display, another glass plate 42 is provided on its innersurface with a transparent display electrode 43, a color filter and ablack matrix independent for each of liquid crystal cells R, G and B. Onthe sides of the electrodes 43 and 44 opposite to the liquid crystallayer 45, there are provided orientation layers, although notillustrated. A polarizing plate 46 is applied over the outer surface ofthe glass plate 41 on the viewing side and a polarizing plate 47 isapplied over the outer surface of the glass plate 42 facing away fromthe viewing side, for instance, with their transmission axesintersecting at right angles. By controlling voltage applied between thetransparent display electrode and the transparent opposite electrode insuch an LCD 40, thereby varying the transmission state, it is possibleto selectively display numerals, characters, symbols, patterns, etc. Inthis case, the reflective diffuser 51 comprises the computer-generatedhologram H, herein referred to as (3), wherein a reflective layer islaminated on a relief pattern having a depth D(x, y) found by expression(7a) for each minute cell having a breadthwise x lengthwise size Δ. Thereflective diffuser 51 is disposed on the side of the LCD 40 facing awayfrom its viewing side. Illumination light 52 incident on the displayside of the LCD 40 and including the desired viewing wavelength range ofλ_(MIN) to λ_(MAX) is diffused and reflected by this reflective diffuser51 in the forward direction, so that white displays can be presented ina bright place without recourse of any spontaneous emission typebackliqht.

The novel computer-generated hologram H of the present invention, hereinreferred to as (3), may be disposed as a reflector between the liquidcrystal layer 45 and a back substrate 42′ in the reflective LCD, asshown in FIG. 18. In this case, the reflective layer 51 of thecomputer-generated hologram H also serves as an optical reflectiveelectrode 44′.

While the novel computer-generated hologram H of the present invention,herein referred to as (3), may be used by itself as a computer-generatedhologram, it is understood that the hologram H may be used as theelemental hologram pieces 2, 2 a-2 c of the computer-generated hologramH shown in FIGS. 1 and 2, wherein the elemental hologram pieces 2, 2 a-2c are closely arranged.

One embodiment of how to form on a substrate a relief pattern preferableto replicate a single computer-generated hologram or acomputer-generated hologram with elemental hologram pieces arrangedclosely (both hereinafter referred to as a computer-generated hologram1) is now explained with reference to FIGS. 19( a) to 19(d) that showtogether one embodiment of forming on a substrate a relief patternpreferable to replicate the computer-generated hologram 1. In thisembodiment, process steps for fabricating photomasks for semiconductorcircuit fabrication, photomask blanks, and lithography systems such aslaser or electron beam lithography systems may be used.

When such a lithography system is used for the computer-generatedhologram 1 wherein the same elemental hologram pieces 2 are arranged,loads on the data processing by the lithography system can be greatlyalleviated by imparting to the lithography system the matrix pitchnecessary for the data on and array of the elemental hologram pieces 2.Loads on calculations for obtaining data on the elemental hologrampieces 2, too, can be greatly reduced as compared with those for theentire computer-generated hologram 1. As already mentioned, if thecomputer-generated hologram 1 has a size of 5 cm×5 cm and each elementalhologram piece 2 has a size of 250 μm×250 μm, the data concerning theelemental hologram piece 2, in area ratio parlance, accounts for barely1/40,000 of the data on the entire computer-generated hologram 1.

First, a photomask blank 10 is obtained by laminating a lowsurface-reflective chromium thin film 12 on a synthetic quartz or othersubstrate 11 having a size of 15 cm×15 cm and a thickness of 6.4 mm. Aresist layer 13 (of the positive type in the illustrated embodiment)resistant to dry etching is provided on the chromium thin film 12 toform a thin film of about 400 nm in thickness as an example. Onematerial for the dry etching resist is ZEP 7000, Nippon Zeon Co., Ltd.The resist layer 13 may be laminated on the chromium thin film 12 byspin coating using a spinner or the like.

The resist layer 13 is then subject to pattern exposure, using a mask 14as shown in FIGS. 19( a) to 19(d).

Alternatively, this pattern exposure may be carried out using a laserlithography system for laser scanning or an electron beam lithographysystem for electron beam scanning. For instance, MEBES 4500 made by ETECmay be used as the electron beam lithography system.

By exposure, an easy-to-dissolve portion 13 b with cured resist resin,and an unexposed portion 13 a are separately formed. Theeasy-to-dissolve portion 13 b is removed by solvent development, e.g.,spray development using a developer spray, thereby forming a resistpattern 13 a.

It is noted here that a negative resist may be used and developerdipping may be used for development. At the subsequent step, not onlydry etching but also wet dip etching may be used, and so the resist isnot always limited to that resistant to dry etching.

Using the formed resist pattern 13 a, resist-free portions of thechromium thin film 12 are dry etched away to leave the underlying quartzsubstrate 11 exposed.

Then, the exposed portions of the quartz substrate 11 are again dryetched. With the progress of etching, a pit 15 is formed along with aprojection having the chromium thin film 12 and resist thin film 13 a inorder from below.

Finally, the resist thin film is dissolved away or otherwise removed toobtain a quartz substrate comprising a pit 15 formed by the etching ofthe starting quartz substrate and a projection 16 with the chromium thinfilm 12 laminated on the top.

This fabrication process itself gives only a binary relief pattern (atwo-step relief pattern including the original quartz substrate surfaceplus one additional different level of surface). By repetition of thephotoetching process comprising resist formation→pattern exposure→resistdevelopment→drying etching of chromium thin film→dry etching of quartzsubstrate→resist removal, however, photoetching can be applied to thepit-and-projection pattern formed by the first photoetching. By controlof etching depth, three levels of surfaces are obtained in addition tothe surface of the original quartz substrate or a total of four levelsof surfaces are achieved.

The resist used herein, for instance, may be an i-line resist based onnovolak resin resistant to dry etching, which is provided in the form ofan about 465 nm thick thin film. The exposure used herein, for instance,may be carried out using ALTA 3500 as a lithography system.

FIGS. 20( a), 20(b) and 20(c) are illustrative of the number ofrepetition of the aforesaid photoething process and the number of stepsproduced thereby. FIG. 20( a) shows that two steps are produced by thefirst photoetching process. By repeatedly applying the photoetchingprocess to the respective upper and lower steps of FIG. 20( a), foursteps at the maximum are obtained, as shown in FIG. 20( b). By a totalof three repetitions of the photoetching process, eight steps at themaximum are obtained as shown in FIG. 20( c).

Thus, steps corresponding in number to the N_(PE)-th power of 2 at themaximum are obtained at the number of repetition of photoetching,N_(PE). It is here noted that the transcript PE stands for photoetching,and N_(PE) is a natural number. Accordingly, the features of thefabrication process should preferably be determined in consideration ofthe relationships between the steps corresponding in number to theN_(PE)-th power of 2, i.e., two, four, eight, sixteen, . . . , steps andthe number of repetition of photoetching, N_(PE), although depending onthe accuracy of the relief pattern and the performance of the obtainedcomputer-generated hologram 1. Even when only one step is added to thenumber of steps corresponding to the N_(PE)-th power of 2, oneadditional photoetching process must be carried out. It is thuspreferable to obtain steps equal or less in number to or than theN_(PE)-th power of 2.

After the given number of steps have been obtained in this way, thechromium thin film is wet etched away to obtain a relief pattern for thecomputer-generated hologram 1, wherein a pit-and-projection pattern witha given number of steps and a given depth is formed on the surface ofthe quartz substrate 11.

For the reproduction of phase distribution data, only re-calculationsare needed. Still, such re-calculations are troublesome, and when thecomputer-generated hologram 1 of the present invention is used for therelief pattern, there is a chance of accidents such as abruptcontamination or breakdown of the computer-generated hologram 1.

It is thus preferable that for fabrication using this type of reliefpattern, one or only a few patterns for replication purposes arefabricated from the first pattern. Then, this replication pattern isused to prepare the necessary number of patterns for fabrication(replication).

To increase the durability of the relief pattern, it is preferable toplate the surface of the relief pattern and then remove a metal-platedpattern therefrom.

Alternatively, the relief pattern may also be fabricated by subjecting asuitable substrate to mechanical engraving using a diamond needle or thelike.

For processes for making a copy of the computer-generated hologram 1using the relief pattern (or, preferably, the aforesaid pattern forfabrication), a process for pressing such a relief pattern 20 as shownin FIG. 21( a) against a resin layer that becomes soft by heating, aninjection process or a casting process may be utilized. Eitherthermoplastic resins or thermosetting resins may be used with theseprocesses.

Preferably on an industrial scale, an uncured resin compositioncontaining an ultraviolet curing resin is positioned in contact with thesurface of the relief pattern 20 (the lower surface of the reliefpattern in FIG. 21( a)). Then, a plastic film providing a substratematerial is laminated on the other side of the resin composition tosandwich the resin composition between the relief pattern and theplastic film. The resin composition is cured by irradiation withultraviolet radiation or other means. Finally, a hologram layer 22comprising the resin layer that has been cured with the surface reliefconfiguration of the relief pattern imparted thereto is releasedtogether with the plastic film 23 to obtain a laminate 21 (FIG. 21( b)).If required, the plastic film 23 may be released off after the curing ofthe resin composition (FIG. 21( c)).

Exemplary ultraviolet curing resins are thermosetting resins such asunsaturated polyester, melamine, epoxy, polyester (meth)acrylate,urethane (meth)acrylate, epoxy (meth)acrylate, polyether (meth)acrylate,polyol (meth)acrylate, melamine (meth)acrylate or triazine acrylate, orionizing radiation curing resins obtained by adding radicalpolymerizable unsaturated monomers to these resin.

For the plastic film 23 providing the substrate material, it ispreferable to use plastic films of excellent transparency andsmoothness. For instance, polyethylene terephthalate films, polyethylenefilms, polypropylene films, polyvinyl chloride films, acrylic films,triacetyl cellulose films and cellulose acetate butylate films may beused, all having a thickness of 1 μm to 1 mm, and preferably 10 μm to100 μm.

As shown in FIGS. 21( a) to 21(e), the laminate 21 copied from therelief pattern 20 with the hologram relief configuration transferredthereto may be used as such. To enhance the optical reflective functionof the laminate 21, however, it is preferable to laminate an opticalreflective layer 24 on the relief surface of the hologram layer 22 (FIG.21( d)) or the lower surface of the plastic film 23. Alternatively, itis acceptable to laminate the optical reflective layer 24 on thenon-relief surface of the hologram 22 (see FIG. 21( e)) when no plasticfilm is used as shown in FIG. 21( c).

For the optical reflective layer 24, two types of reflective layers,i.e., a metal reflective layer formed of a metal thin film opaque tolight or the like (which layer shows transparency at a very smallthickness), and a transparent reflective layer which is transparent tolight and has a refractive index different from that of the hologramlayer, may be used.

The metal reflective layer may be formed by sole or combined use ofmetals such as Cr, Fe, Co, Ni, Cu, Ag, Au, Ge, Al, Mg, Sb, Pb, Cd, Bi,Sn, Se, In, Ga and Rb, or oxides or nitrides thereof.

Of these, Al, Cr, Ni, Ag, and Au are most preferred.

When the optical reflective layer is formed of a metal thin film, it ispreferable to use thin-film techniques such as vacuum evaporation,sputtering, and ion plating.

At a thickness of 200 Å or less, the reflective layer meets its ownfunction although it has relatively high light transmittance andtransparency as well.

Alternatively, the optical reflective layer may be formed of acontinuous thin film of material having a refractive index differentfrom that of the hologram layer 22. The continuous thin film has athickness small enough to make a thin-film forming material transparent,but should preferably have a thickness of usually 100 to 1,000 Å. Thecontinuous thin film may be formed on the relief surface by thin-filmtechniques such as vacuum evaporation, sputtering, and ion plating. Thecontinuos thin film may have a refractive index lower or higher thanthat of the hologram layer 22; however, the difference in refractiveindex between both should be preferably at least 0.3, more preferably atleast 0.5, and even more preferably at least 1.0.

A continuous thin film having a refractive index higher than that of thehologram layer 22 may be formed of ZnS, TiO₂, Al₂O₃, Sb₂S₃, SiO, TiO,SiO₂ or the like. A continuous thin film having a refractive index lowerthan that of the optical diffractive structure layer may be formed ofLiF, MgF₂, AlF₃ or the like. In addition, transparent synthetic resinshaving a refractive index different from that of the optical diffractivestructure layer, for instance, polytetrafluoroethylene,polychlorotrifluoroethylene, polyvinyl acetate, polyethylene,polypropylene and polymethyl methacrylate may be used for the opticalreflective layer.

It is here noted that if innumerable fine pores are provided by laserlithography or other suitable means through the optical reflective layerformed as a metal reflective layer (which itself is opaque to light), itis then possible to ensure light transmission simultaneously withoptical reflectivity. Such a metal reflective layer may also be used forthe present invention.

As shown in FIGS. 21( a) to 21(e), the computer-generated hologram 1 ofthe present invention is made up of the hologram layer 22 alone or thehologram laminate 21 comprising the hologram layer 22 and the plasticfilm 23. The optical reflective layer 24 may be laminated on the upper(relief) or lower surface of the hologram layer 22 or hologram laminate21. These hologram products ate all effectively applied to displaydevices, esp., LCD devices.

FIG. 22( a) shows an embodiment wherein the computer-generated hologram1 is applied to the non-viewing side of an LCD 30. The LCD 30 comprises,in order from its upper surface side, a polarizing plate 31, a glasssubstrate 32, a transparent electrode 33, a liquid crystal layer 34, atransparent electrode 33′, a glass substrate 32′ and a polarizing plate31′ which are laminated together. The computer-generated hologram 1 isdisposed on the back side of the LCD 30. In FIG. 22( a), thecomputer-generated hologram 1 consisting of the hologram layer 22 aloneis provided. However, it is noted that any one of the hologram productsshown in FIGS. 21( a) to 21(d) may be used.

When the computer-generated hologram 1 is applied to an LCD, it may beapplied between the liquid crystal layer 34 and the underlying backsubstrate. Alternatively, the computer-generated hologram 1 comprisingthe optical reflective layer 24 and hologram layer 22 may be disposed onthe lower surface of the liquid crystal layer 34, as shown in FIG. 22(b).

As a matter of course, any one of the hologram products shown in FIGS.21( b) to 21(e) may be used as the computer-generated hologram 1.

Reference is then made to a computer-generated hologram comprising atransparent plate material having a light refractive index higher thanthat of air and a blaze pattern of sawtoothed shape in section, whichblaze pattern is disposed on the back surface of the transparent plate.The computer-generated hologram is designed in such a way that the depthd of the blaze is equivalent to a half wavelength or d=λ/2n wherein λ isthe wavelength of reference light and n is the light refractive index ofthe transparent plate. This computer-generated hologram can providesolutions to prior art problems in conjunction with diffractionefficiency, master pattern fabrication and replication, andapplications. Thus, the present invention provides such acomputer-generated hologram as well as a reflector and a reflective LCDconstructed using the same. In what follows, too, both such acomputer-generated hologram and a computer-generated hologram whereinelemental hologram pieces are closely arranged will be referred to asthe computer-generated hologram 1.

Referring to FIG. 23( a), the computer-generated hologram 1 comprises atransparent plate and a hologram layer 22 having a blaze pattern 22 atherefor, which layer is disposed on the lower surface of thetransparent plate. The so-called blaze pattern 22 a comprises aplurality of grooves of sawtoothed shape in section, each comprising aportion 22 b slanting with respect to the transparent plate and aportion 22 c vertical with respect to the transparent plate. As viewedin a vertical direction to the transparent plate, the blaze pattern hasa depth d.

An optical reflective layer 24 is laminated on and along the blazepattern 22 a of the computer-generated hologram 1. Referring to FIG. 23(a), light 3 entered into the hologram 1 from above the paper isreflected at the interface between the hologram layer 22 and the opticalreflective layer 24, as indicated at 4, emerging upward from thehologram 1.

The length of an optical path in the hologram layer 22 taken by thelight entering and emerging from the computer-generated hologram 1 makesa difference of 2n times as much as the depth d of the blaze pattern(where n is the light refractive index of the medium, i.e., thetransparent plate) at the maximum. When this difference in optical pathlength coincides with the wavelength λ of the incident light, thediffraction efficiency reaches a maximum. Thus, λ=2nd or d =λ/2n.

FIG. 23( b) illustrates another embodiment of the computer-generatedhologram 1, wherein the section of each of grooves in a sawtoothed blazepattern 22 a does not have a sawtoothed configuration defined by smoothlines. In this embodiment, the oblique side of each sawtooth comprises aportion 22 b parallel with a transparent plate and a portion 22 cvertical to the transparent plate. Then, these portions 22 b and 22 care repeatedly formed until 4 steps are obtained. This blaze pattern 22a is a so-called binary pattern. Here the number of steps (N) is thenumber of all steps having different heights, and the number ofdifferences in level is N−1.

The blaze pattern 22 a comprising a plurality of grooves, each formedstepwise, has a diffractive action equivalent to that of an assumedsawtoothed blaze pattern 22 a′ having a depth d′, as shown by one-dottedlines in FIG. 23( b). In the case of the blaze pattern 22 a′,interference of light occurs when λ=2nd′. In other words, d′=λ/2n.

However, the actual depth d of each groove formed stepwise in the blazepattern 22 a of the computer-generated hologram is smaller than theassumed d′ by one step or, for the assumed d′,d=d′×{(N−1)/N}=(λ/2)×{(N−1)/N}. It follows that d=λ(N−1)/2nN.

With the sawtoothed blaze pattern provided in a stepwise form having Nsteps, a computer-generated hologram having an equivalent diffractiveaction is thus obtainable even when the groove depth d is 1/N smallerthan that of the blaze pattern of smooth shape in section, as shown inFIG. 23( a).

In the computer-generated holograms of whether the blaze type or thebinary type, the groove depth d is inversely proportional to the lightrefractive index, n, of the transparent plate forming part of thehologram layer 22. Therefore, if a material having a high lightrefractive index is used, it is then possible to decrease the groovedepth d. For instance, a blaze type of computer-generated hologramfabricated using an acrylic resin having a light refractive index of 1.4has a groove depth of d=500 nm/(2×1.4) or about 180 nm with the provisothat the reference wavelength is 500 nm.

Here consider the case where light is entered into the same blaze typeof computer-generated hologram from below. Since the medium is air(n=1), d=500 nm/2=250 nm. That is, the groove depth increases by lessthan 40% as compared with the case where light is entered thereinto fromabove, and so a master blaze pattern is more difficult to fabricate andreplicate.

For such computer-generated holograms as shown in FIGS. 23( a) and23(b), any one of the aforesaid computer-generated holograms (1) to (3)may be used. In the computer-generated hologram (1), (2) or (3), onesingle hologram may be formed all over the surface. Alternatively,identical minute elemental hologram pieces may be closed arranged allover the surface (FIGS. 1 and 2).

For processes for making a copy of such a computer-generated hologram 1as shown in FIG. 23( a) or 23(b) using the blaze pattern (or,preferably, the aforesaid pattern for fabrication), a process forpressing such a blaze pattern 20 as shown in FIG. 24( a) against a resinlayer that becomes soft by heating, an injection process or a castingprocess may be utilized. Either thermoplastic resins or thermosettingresins may be used with these processes.

Preferably on an industrial scale, an uncured resin compositioncontaining an ultraviolet curing resin is positioned in contact with thesurface of the blaze pattern 20 (the lower surface of the relief patternin FIG. 24( a)) by means of coating or the like. Then, a plastic film 23providing a substrate material is put on the resin composition whilecare is taken to remove air bubbles, if any. Pressure is then applied onthe plastic film 23 from above, using a roll or the like, to laminatethe plastic film 23 on the blaze pattern surface with the requiredthickness of uncured resin composition layer 22 d interposed betweenthem.

While the uncured resin composition layer 22 d is sandwiched between thesurface of the blaze pattern 20 and the plastic film 23, the resincomposition layer is cured by irradiation with ultraviolet radiation orother means to prepare a laminate 21 comprising a hologram layer 22comprising the resin layer that has been cured with the surface blazeconfiguration of the blaze pattern imparted thereto. Thereafter, thelaminate 21 is released from the blaze pattern 20 (FIG. 24( b)). Ifrequired, the plastic film 23 may be released off after the curing ofthe resin composition (FIG. 24( c)).

The “transparent plate” used herein is understood to refer to not onlythe hologram layer 22 alone but also the laminate 21 comprising thehologram layer 22 and plastic film 23.

Exemplary ultraviolet curing resins are thermosetting resins such asunsaturated polyester, melamine, epoxy, polyester (meth)acrylate,urethane (meth)acrylate, epoxy (meth)acrylate, polyether (meth)acrylate,polyol (meth)acrylate, melamine (meth)acrylate or triazine acrylate, orionizing radiation curing resins obtained by adding radicalpolymerizable unsaturated monomers to these resins. It is here notedthat curing may also be carried out using electron beams in place ofultraviolet radiation.

For the plastic film 23 providing the substrate material, it ispreferable to use plastic films of excellent transparency andsmoothness. For instance, transparent synthetic resin films such aspolyethylene terephthalate films, polyethylene films, polypropylenefilms, polyvinyl chloride films, acrylic films, triacetyl cellulosefilms and cellulose acetate butylate films may be used, all having athickness of 1 μm to 1 mm, and preferably 10 μm to 100 μm.

The laminate 21 (FIG. 24( b) copied from the blaze pattern 20 with thehologram relief configuration transferred thereto or the hologram layer22 free from the plastic film 23 (FIG. 24( c)) is used while the surfacefree from the hologram blaze pattern (the upper surface in FIGS. 24( b)and 24(c)) is utilized as the viewing side.

These may be used as such. To enhance the optical reflecting function,however, it is preferable to laminate an optical reflective layer 24 onthe blaze surface of the hologram layer 22 (FIG. 24( d)).

For the optical reflective layer 24, two types of reflective layers,i.e., a metal reflective layer formed of a metal thin film opaque tolight or the like (which layer shows transparency at a very smallthickness), and a transparent reflective layer which is transparent tolight and has a light refractive index different from that of thehologram layer, may be used.

The metal reflective layer may be formed by sole or combined use ofmetals such as Cr, Fe, Co, Ni, Cu, Ag, Au, Ge, Al, Mg, Sb, Pb, Cd, Bi,Sn, Se, In, Ga and Rb, or oxides or nitrides thereof. Of these, Al, Cr,Ni, Ag, and Au are most preferred.

When such a thin film is used to form the optical reflective layer onthe blaze surface of the hologram layer, it is preferable to use thinfilm techniques such as vacuum evaporation, sputtering, and ion plating.

At a thickness of 200 Å or less, the reflective layer meets its ownfunction although it has relatively low light transmittance andtransparency as well.

Alternatively, the optical reflective layer may be a transparentreflective layer formed of a continuous thin film of material having alight refractive index different from that of the hologram layer 22.

The transparent reflective layer has a thickness small enough to make athin-film forming material transparent, but should preferably have athickness of usually 100 to 1,000 Å.

The transparent reflective layer may be formed on the blaze surface ofthe hologram layer by thin-film techniques such as vacuum evaporation,sputtering, and ion plating, as in the case of the metal reflectivelayer.

The transparent reflective layer may have a refractive index lower orhigher than that of the hologram layer 22; however, the difference inrefractive index between both should be preferably at least 0.3, morepreferably at least 0.5, and even more preferably at least 1.0.

A continuous thin film having a refractive index higher than that of thehologram layer 22 may be formed of ZnS, TiO₂, Al₂O₃, Sb₂S₃, SiO, TiO,SiO₂ or the like. A continuous thin film having a refractive index lowerthan that of the hologram layer 22 may be formed of LiF, MgF₂, AlF₃ orthe like.

In addition, transparent synthetic resins having a refractive indexdifferent from that of the hologram layer 22, for instance,polytetrafluoroethylene, polychlorotrifluoroethylene, polyvinyl acetate,polyethylene, polypropylene and polymethyl methacrylate may be used forthe optical reflective layer. These resins, upon dissolved in solvents,may be laminated on the blaze surface of the hologram layer 22 by meansof coating or the like.

It is here noted that if innumerable fine pores are provided by laserlithography or other suitable means through the optical reflective layerformed as a metal reflective layer (which itself is opaque to light), itis then possible to ensure light transmission simultaneously withoptical reflectivity. Such a metal reflective layer may also be used asthe optical reflective layer 24 the present invention.

When the optical reflective layer 24 is laminated on the blaze patternside of the hologram layer 22, it is a prerequisite that light berefracted at the interface between the hologram layer 22 and the opticalreflective layer; the optical reflective layer 24 be free from anylamination defects such as pinholes along the blaze pattern. As long asthe optical reflective layer 24 has the required minimum thickness,slight thickness variations in the optical reflective layer 24 areacceptable. It is thus possible to alleviate loads on control in theprocess of fabricating the optical reflective layer 24.

Depending on whether or not the plastic film 23 and/or opticalreflective layer 24 are provided, such a computer-generated hologram 1as shown in FIG. 23( a) or 23(b) may comprise the hologram laminate 21(FIG. 24( b)), the hologram layer 22 alone (FIG. 24( c)), and thehologram layer 22 with the optical reflective layer 24 laminated on thelower surface of the hologram layer 22. These hologram products are alleffectively applied to display devices, esp., LCDs, while the blaze-freesurface side of the hologram layer 22 is used as a viewing side.

FIG. 25( a) shows an embodiment of the present invention, wherein thecomputer-generated hologram 1 is applied to the non-viewing side of anLCD 30 that is a main pat of a liquid crystal display system. The LCD 30comprises, in order from its upper surface side, a polarizing plate 31,a glass substrate 32, a transparent electrode 33, a liquid crystal layer34, a transparent electrode 33′, a glass substrate 32′ and a polarizingplate 31′ which are laminated together. The computer-generated hologram1 is disposed on the back side of the LCD 30. In FIG. 25( a), thecomputer-generated hologram 1 made up of a hologram laminate consistingof the hologram layer 22 and optical reflective layer 24 is provided.However, it is noted that the aforesaid types of holograms may all beused.

As shown in FIG. 25( a), the computer-generated hologram 1 may bepositioned parallel with and in contact with, not spaced away from, theLCD 30. Alternatively, the computer-generated hologram 1 may belaminated on the LCD 30 with an adhesive layer applied between the uppersurface of the computer-generated hologram 1 and the polarizing plate31′. Preferably in this case, the adhesive layer is previously laminatedon the upper surface (the blaze pattern-free surface of the hologramlayer) of the computer-generated hologram 1. It is then preferable touse an adhesive layer of high transparency.

When such a computer-generated hologram 1 as shown in FIG. 23( a) or23(b) is applied to an LCD, it may be applied between the liquid crystallayer 34 and the underlying back substrate. Alternatively, thecomputer-generated hologram 1, wherein the optical reflective layer 24,hologram layer 22 and adhesive layer 25 are laminated together in thisorder, may have previously been disposed on the lower surface of theliquid crystal layer 34, as shown in FIG. 25( b).

As a matter of course, any one of the hologram products shown in FIGS.24( b) to 24(e) may be used as the computer-generated hologram 1, withor without the adhesive layer laminated on the surface thereof.

The aforesaid computer-generated hologram 1, because of having a smoothupper surface, can be brought in perfect contact with the back surface,etc. of a display device without any possible slanting of the hologram 1or any possible isolation of the hologram 1 from the back surface, sothat useless interference of light can be eliminated.

When such a computer-generated hologram 1 as shown in FIG. 23( a) or23(b) is applied to a display device such as an LCD, it is preferable tomake the light refractive index of the display device substantiallyequal to that of the computer-generated hologram (exclusive of anoptical reflective layer, if any). When the computer-generated hologramand LCD are laminated together with an adhesive layer interleavedbetween them, it is preferred that the LCD, computer-generated hologram(exclusive of an optical reflective layer, if any) and adhesive layerhave a substantially identical light refractive index.

It is here noted that the adhesive layer interleaved between thecomputer-generated hologram 1 and an LCD or other display device isunderstood to include a tackifier layer.

Since such a computer-generated hologram 1 as shown in FIG. 23( a) or23(b) is used while the viewing side is defined by the hologram layer 22or plastic film 23, it is preferable to form an antireflection coatingon the outermost surface of the hologram 1, viz., the surface of thehologram layer 22 or plastic film 23.

Referring here to a typical antireflection coating, a transparentconductive thin film having an antistatic function and comprising indiumtin oxide (In₂O₃ doped with tin, called ITO) or the like is laminated onthe outermost surface of the computer-generated hologram 1, and anantireflection, low-refractive-index thin film having a refractive indexlower than that of the transparent conductive thin film, e.g., an SiO₂thin film is formed on the transparent conductive thin film. Inaddition, a polymethyl methacrylate resin or other hard coating layermay be interposed between the aforesaid outermost surface and the thinfilm for the purpose of preventing any possible injuring.

In this case, it is more preferable to use a plastic film comprising amultilayer dielectric material (for instance, HEBBAR coating made byMeresglio Co., Ltd., U.S.A.).

As can be appreciated from the foregoing explanations, thecomputer-generated hologram provided to achieve the first object of thepresent invention is constructed such that, in a range of wavelengthsincluding the reference wavelength wherein zero-order transmission lightor zero-order reflection light incident on the computer-generatedhologram at a given angle of incidence is seen in white by additivecolor mixing, the maximum diffraction angle of incident light of theminimum wavelength in said range and incident at said angle of incidenceis larger than the minimum diffraction angle of incident light of themaximum wavelength in said range and incident at said angle ofincidence. Thus, the computer-generated hologram can be seen in white inthe angle range defined between the maximum diffraction angle of theminimum wavelength and the minimum diffraction angle of the maximumwavelength, and there is no change in the color seen even when theviewer moves his eyes within that range. This computer-generatedhologram is suitable for reflector in reflective LCDs.

According to the twelfth invention to achieve the second object of theinvention, there is provided a computer-generated hologram comprising anarray of identical elemental hologram pieces. It is thus possible toprovide a computer-generated hologram which can reduce the length oftime required for calculations and relief pattern fabrication ingeneral, and exposure for photoetching in particular.

According to the thirteenth invention, there is provided acomputer-generated hologram which, in addition to having the effect ofthe twelfth invention, can be seen in white in a wider range.

According to the fourteenth invention, there is provided acomputer-generated hologram which, in addition to the effect of the 12thor 13th invention, have the ability to diffract both vertically incidentlight and obliquely incident light in the vertical direction.

According to the fifteenth invention, there is provided acomputer-generated hologram which, in addition to the effect of the 12thor 13th invention, has the ability to diffract obliquely incident lighttoward a given viewing region and vertically incident light towardanother viewing region.

According to the sixteenth invention, there is provided acomputer-generated hologram which, in addition to the effect of any oneof the 12th to 15th inventions, have a simple structure comprising ahologram layer alone.

According to the seventeenth invention, there is having the effect ofthe 16th invention, has strong strength (because the hologram layer issupported by the transparent substrate) and can be advantageouslyfabricated (because the resin composition for forming the hologram layeris covered).

According to the eighteenth invention, there is provided acomputer-generated hologram which, in addition to having the effect ofany one of the 12th to 17th inventions, can efficiently be fabricated bythe replication of the relief pattern (because the hologram is formed bythe relief pattern on the surface of the hologram-forming layer.

According to the 19th or 20th invention, there is provided acomputer-generated hologram which, in addition to the effect of the 18thinvention, has a high optical diffraction effect because of thelamination of the optical reflective layer.

According to the 21st invention, there is provided a reflector havingthe same effect as that of the computer-generated hologram according toany one of the 12th to 20th inventions.

According to the 22nd or 23rd invention, there is provided a reflectiveliquid crystal display with the effect of the reflector according to the21st invention added thereto.

According to the 24th invention, there is provided a computer-generatedhologram fabrication process using the technique well fit fordetermining a hologram having the desired diffraction effect andtransforming the obtained results into a relief pattern.

According to the 25th invention, there is provided a computer-generatedhologram fabrication process which, in addition to having the sameeffect as in the 24th invention, enables a relief pattern to beefficiently formed depending on the depth and the number of stepsobtained by transformation.

According to the 26th invention, there is provided a computer-generatedhologram fabrication process which, in addition to having the effect ofthe 24th or 25th invention, can simplify the computation of phasedistribution and depth and the formation of the relief pattern and canreduce computation loads on a lithography system such as a laser lightor electron beam lithography system so that the relief pattern can beformed within a short time. This is because the phase distribution canbe determined per elemental hologram piece rather than for the entirehologram, and the relief pattern is formed on the basis of the phasedistribution obtained by repeatedly arranging the found phasedistribution in the longitudinal direction of the substrate.

According to the 27th invention, there is provided a process which, inaddition to having the effect of any one of the 24th to 26th inventions,enables a computer-generated hologram of high diffraction efficiency tobe fabricated by the addition of the step of forming the opticalreflective layer.

According to the 28th invention, there is provided a process for theefficient fabrication of a computer-generated hologram which does notonly have the effect of any one of the 24th to 27th inventions, but alsoenables more steps to be obtained by a lesser number of photoetchingcycles, because the number of steps L is given by the N-th power of 2where N is the number of photoetching cycles.

According to the 29th invention to achieve the third object, there isprovided a computer-generated hologram having a blaze pattern ofsawtoothed shape in section. As in the case of a rainbow hologram, thiscomputer-generated hologram is not affected by interference fringesresulting from higher-order light other than first-order light, so thathigh optical diffraction efficiency can be obtained. The blaze patternis formed on the back side of the transparent plate so that lightreciprocates in the transparent plate having a refractive index higherthan that of air. Accordingly, the depth of the blaze pattern can bemade smaller as compared with the case where the blaze pattern is formedon the front side of the transparent plate. In addition, the opticalreflective layer can be formed with no care taken of thicknessvariations, etc.

According to the 30th invention, there is provided a computer-generatedhologram having a blaze pattern of stepwise sawtoothed shape in section,which has much the same effect as that of the 29th invention.

According to the 31st invention, there is provided a computer-generatedhologram which, in addition to the effect of the 29th or 30th invention,has more improve optical reflectivity achieved by the lamination of theoptical reflective layer on and long the back side of the transparentplate.

According to the 32nd invention, there is provided a computer-generatedhologram which does not only have the effect of any one of the 29th to31st inventions but is also subject to antireflection treatment, therebypreventing the reflection of so-called ambient extraneous light orincident light for reflection at the front surface of the transparentplate or the useless reflection and, hence, wasteful consumption of apart of the necessary incident light.

According to the 33rd invention, there is provided a reflector which hasthe effect of any one of the 29th to 32nd inventions.

According to the 34th invention, there is provided a reflector which, inaddition to having the effect of the 33rd invention, can be easilymounted on the back surface of a display device such as a liquid crystaldisplay device through the transparent adhesive layer laminated on thefront surface of the transparent plate.

According to the 35th invention, there is provided a reflective liquidcrystal display which comprises a reflector having the effect of the33rd invention, so that images can be displayed with high reflectionefficiency and high contrast.

According to the 36th invention, there is provided a reflective liquidcrystal display wherein the reflector having the effect of the 34thinvention is laminated on the back side thereof with the transparentadhesive layer interleaved therebetween, so that images can be displayedwith high optical reflection efficiency and high contrast, and thereflector can easily and surely be laminated on the liquid crystaldisplay.

According to the 37th invention, there is provided a reflective liquidcrystal display which, in addition to having the effect of the 35th or36th invention, is free from useless diffraction because the parts usedhave a substantially identical light refractive index.

According to the 38th invention, there is provided a reflective liquidcrystal display in which the reflector having the effect of the 33rdinvention is built, so that images can be displayed with high opticalreflection efficiency and high contrast.

According to the 39th invention, there is provided a reflective liquidcrystal display in which the reflector having the effect of the 33rdinvention is applied to a light transmission display so that images canbe displayed with high optical reflection efficiency and high contrast.

1. A computer-generated hologram, wherein a blaze pattern of sawtoothedshape in section is formed on a back surface of a transparent substrateand a depth d of said blaze pattern is d=λ/2n where λ is the wavelengthof reference light and n is a light refractive index of a materialforming said transparent substrate, wherein an optical reflective layeris laminated on and along said blaze pattern formed on the back surfaceof said transparent substrate; wherein the hologram does not focusincident light on one point.
 2. The computer-generated hologramaccording to claim 1, wherein a front surface of said transparentsubstrate has been subject to antireflection treatment.
 3. A reflectorwhich uses the computer-generated hologram according to claim
 2. 4. Areflective liquid crystal display, including the reflector according toclaim 3, wherein said liquid crystal display device, said transparentadhesive layer and said transparent substrate in said reflector have asubstantially identical light refractive index.
 5. A reflector whichuses the computer-generated hologram according to claim
 1. 6. Areflector which uses a computer-generated hologram, wherein a blazepattern of sawtoothed shape in section is formed on a back surface of atransparent substrate and a depth d of said blaze pattern is d=λ/2nwhere λ is the wavelength of reference light and n is a light refractiveindex of a material forming said transparent substrate; wherein thehologram does not focus incident light on one point.
 7. The reflectoraccording to claim 6, claim 5, or claim 3, wherein a transparentadhesive layer is laminated on a front surface of said transparentsubstrate.
 8. A reflective liquid crystal display, wherein said frontsurface of the reflector according to claim 7 is laminated on a backsurface of a liquid crystal display device with said transparentadhesive layer interposed therebetween.
 9. The computer-generatedhologram according to claim 1 or claim 2, wherein the blaze patterncomprises minute elemental hologram pieces.
 10. A reflective liquidcrystal display, wherein said front surface of the reflector accordingto claim 6, claim 5, or claim 3 is in close contact with a back surfaceof a liquid crystal display device.
 11. A reflective liquid crystaldisplay including the reflector of claim 6, claim 5, or claim 3, whereinthe liquid crystal display device and said transparent substrate in saidreflector have a substantially identical light refractive index.
 12. Areflective liquid crystal display, including the reflector of claim 6,claim 5, or claim 3, wherein the computer-generated hologram isinterposed between a liquid crystal layer and a back substrate with afront surface of said computer-generated hologram opposite to saidliquid crystal layer.
 13. A reflective display, wherein said frontsurface of the reflector according to claim 6, claim 5, or claim 3, isin close contact with a back surface of a light transmission display.